Problem: $\dfrac{ -6g - 10h }{ -4 } = \dfrac{ 6g - 8i }{ -6 }$ Solve for $g$.
Explanation: Multiply both sides by the left denominator. $\dfrac{ -6g - 10h }{ -{4} } = \dfrac{ 6g - 8i }{ -6 }$ $-{4} \cdot \dfrac{ -6g - 10h }{ -{4} } = -{4} \cdot \dfrac{ 6g - 8i }{ -6 }$ $-6g - 10h = -{4} \cdot \dfrac { 6g - 8i }{ -6 }$ Multiply both sides by the right denominator. $-6g - 10h = -4 \cdot \dfrac{ 6g - 8i }{ -{6} }$ $-{6} \cdot \left( -6g - 10h \right) = -{6} \cdot -4 \cdot \dfrac{ 6g - 8i }{ -{6} }$ $-{6} \cdot \left( -6g - 10h \right) = -4 \cdot \left( 6g - 8i \right)$ Distribute both sides $-{6} \cdot \left( -6g - 10h \right) = -{4} \cdot \left( 6g - 8i \right)$ ${36}g + {60}h = -{24}g + {32}i$ Combine $g$ terms on the left. ${36g} + 60h = -{24g} + 32i$ ${60g} + 60h = 32i$ Move the $h$ term to the right. $60g + {60h} = 32i$ $60g = 32i - {60h}$ Isolate $g$ by dividing both sides by its coefficient. ${60}g = 32i - 60h$ $g = \dfrac{ 32i - 60h }{ {60} }$ All of these terms are divisible by $4$ $g = \dfrac{ {8}i - {15}h }{ {15} }$